- Theory of elliptic PDEs,
- Viscosity solutions,
- The direct method in the Calculus of Variations,
- Bochner integrals and parabolic theory.

- Lecturer: Ben Pooley.
- Lectures via TCC, 1400-1600 on Wednesdays, and for 8 weeks starting on 22/01/2020.
- Assessment will be via an essay relating to one of the topics covered (details TBC).

- Lecture 1: Elliptic PDEs 1 (weak solutions) [pdf]
- Lecture 2: Elliptic PDEs 2 (existence and regularity) [pdf]
- Lecture 3: Variational methods 1 [pdf] [addendum]
- Lecture 4: Variational methods 2 [pdf]
- Lecture 5: Variational methods 3 [pdf]
- Lecture 6: Parabolic theory 1 [pdf]
- Lecture 7: Parabolic theory 2 [pdf]
- Lecture 8: Parabolic theory 3 [pdf]
- Digression: Navier-Stokes in 3D [pdf]

- Sobolev Spaces Pure and Applied Mathematics vol. 140 Elsevier Amsterdam 2003
- Lecture Notes on "Partial Differential Equations 2 Variational Methods" 2016 [link]
- Partial Differential Equations Graduate Studies in Mathematics vol. 19 AMS 1998
- Elliptic partial differential equations of second order Grundlehren der Mathematischen Wissenschaften vol. 224 Springer, Berlin 1983
- Functional Analysis Pure and Applied Mathematics Wiley-Interscience, New York 2002
- Calculus of Variations Universitext Springer, Cham 2018
- Infinite-Dimensional Dynamical Systems Cambridge texts in applied mathematics CUP 2001
- Nonlinear partial differential equations with applications International Series of Numerical Mathematics, 153. Springer Basel 2013
- Singular integrals and differentiability properties of functions Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970